Description: Two ways of expressing "exactly one" element. (Contributed by Zhi Wang, 23-Sep-2024)
Ref | Expression | ||
---|---|---|---|
Assertion | reutru | |- ( E! x x e. A <-> E! x e. A T. ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | tru | |- T. |
|
2 | 1 | biantru | |- ( x e. A <-> ( x e. A /\ T. ) ) |
3 | 2 | eubii | |- ( E! x x e. A <-> E! x ( x e. A /\ T. ) ) |
4 | df-reu | |- ( E! x e. A T. <-> E! x ( x e. A /\ T. ) ) |
|
5 | 3 4 | bitr4i | |- ( E! x x e. A <-> E! x e. A T. ) |